Before WWII there were Ilford, Gevaert, and Kodak deep tank photofinishing developers with 3 developing agents, they used a small amount of Pyrogallol as an oxygen scavenger, it's supposed to have given a cleaner working developer.
There's also the excellent developers Johnsons used to make and sell in the UK using Meritol effectively a fusion of PPD and Pyrocatechin along with another developing agent. So 3 developing agents is not uncommon but 5 is someone having a joke at the expense of those who believe what's being suggested.
Ian